Statistics For Dummies

Deborah J. Rumsey, PhD, is Professor of Statistics and Statistics Education Specialist at The Ohio State University. She is the author of Statistics Workbook For Dummies, Statistics II For Dummies, and Probability For Dummies.

• Introduction 1About This Book 1Conventions Used in This Book 2What You’re Not to Read 3Foolish Assumptions 3How This Book Is Organized 3Part 1: Vital Statistics about Statistics 3Part 2: Number-Crunching Basics 4Part 3: Distributions and the Central Limit Theorem 4Part 4: Guesstimating and Hypothesizing with Confidence 4Part 5: Statistical Studies and the Hunt for a Meaningful Relationship 5Part 6: The Part of Tens 5Icons Used in This Book 6Where to Go from Here 6Part 1: Vital Statistics About Statistics 7Chapter 1: Statistics in a Nutshell 9Thriving in a Statistical World 10Designing Appropriate Studies 11Surveys 11Experiments 12Collecting Quality Data 13Selecting a good sample 13Avoiding bias in your data 14Creating Effective Summaries 14Descriptive statistics 15Charts and graphs 15Determining Distributions 16Performing Proper Analyses 17Margin of error and confidence intervals 18Hypothesis tests 19Correlation, regression, and two-way tables 20Drawing Credible Conclusions 21Reeling in overstated results 21Questioning claims of cause and effect 21Becoming a Sleuth, Not a Skeptic 22Chapter 2: The Statistics of Everyday Life 23Statistics and the Media: More Questions than Answers? 24Probing popcorn problems 24Venturing into viruses 24Comprehending crashes 25Mulling malpractice 26Belaboring the loss of land 26Scrutinizing schools 27Studying sports 28Banking on business news 28Touring the travel news 29Surveying sexual stats 29Breaking down weather reports 30Musing about movies 30Highlighting horoscopes 31Using Statistics at Work 31Delivering babies — and information 31Posing for pictures 32Poking through pizza data 32Statistics in the office 33Chapter 3: Taking Control: So Many Numbers, So Little Time 35Detecting Errors, Exaggerations, and Just Plain Lies 36Checking the math 36Uncovering misleading statistics 37Looking for lies in all the right places 44Feeling the Impact of Misleading Statistics 44Chapter 4: Tools of the Trade 47Statistics: More than Just Numbers 47Grabbing Some Basic Statistical Jargon 49Data 50Data set 51Variable 51Population 51Sample, random, or otherwise 52Statistic 54Parameter 54Bias 55Mean (Average) 55Median 56Standard deviation 56Percentile 57Standard score 57Distribution and normal distribution 58Central Limit Theorem 59z-values 60Experiments 60Surveys (Polls) 62Margin of error 62Confidence interval 63Hypothesis testing 64p-values 65Statistical significance 66Correlation versus causation 67Part 2: Number-Crunching Basics 69Chapter 5: Means, Medians, and More 71Summing Up Data with Descriptive Statistics 71Crunching Categorical Data: Tables and Percents 72Measuring the Center with Mean and Median 75Averaging out to the mean 75Splitting your data down the median 77Comparing means and medians: Histograms 78Accounting for Variation 80Reporting the standard deviation 81Being out of range 84Examining the Empirical Rule (68-95-99.7) 85Measuring Relative Standing with Percentiles 87Calculating percentiles 88Interpreting percentiles 89Gathering a five-number summary 93Exploring interquartile range 94Chapter 6: Getting the Picture: Graphing Categorical Data 95Take Another Little Piece of My Pie Chart 96Tallying personal expenses 96Bringing in a lotto revenue 97Ordering takeout 98Projecting age trends 99Raising the Bar on Bar Graphs 101Tracking transportation expenses 101Making a lotto profit 103Tipping the scales on a bar graph 104Pondering pet peeves 105Chapter 7: Going by the Numbers: Graphing Numerical Data 107Handling Histograms 108Making a histogram 108Interpreting a histogram 111Putting numbers with pictures 115Detecting misleading histograms 117Examining Boxplots 120Making a boxplot 120Interpreting a boxplot 121Tackling Time Charts 127Interpreting time charts 127Understanding variability: Time charts versus histograms 128Spotting misleading time charts 128Part 3: Distributions And The Central Limit Theorem 133Chapter 8: Random Variables and the Binomial Distribution 135Defining a Random Variable 136Discrete versus continuous 136Probability distributions 137The mean and variance of a discrete random variable 138Identifying a Binomial 139Checking binomial conditions step by step 140No fixed number of trials 140More than success or failure 141Trials are not independent 141Probability of success (p) changes 141Finding Binomial Probabilities Using a Formula 142Finding Probabilities Using the Binomial Table 144Finding probabilities for specific values of X 145Finding probabilities for X greater-than, less-than, or between two values 146Checking Out the Mean and Standard Deviation of the Binomial 146CHAPTER 9: The Normal Distribution 149Exploring the Basics of the Normal Distribution 150Meeting the Standard Normal (Z-) Distribution 152Checking out Z 153Standardizing from X to Z 153Finding probabilities for Z with the Z-table 155Finding Probabilities for a Normal Distribution 156Finding X When You Know the Percent 158Figuring out a percentile for a normal distribution 159Translating tricky wording in percentile problems 161Normal Approximation to the Binomial 162CHAPTER 10: The t-Distribution 165Basics of the t-Distribution 165Comparing the t- and Z-distributions 165Discovering the effect of variability on t-distributions 167Using the t-Table 167Finding probabilities with the t-table 168Figuring percentiles for the t-distribution 168Picking out t*-values for confidence intervals 169Studying Behavior Using the t-Table 170Chapter 11: Sampling Distributions and the Central Limit Theorem 171Defining a Sampling Distribution 172The Mean of a Sampling Distribution 174Measuring Standard Error 174Sample size and standard error 175Population standard deviation and standard error 176Looking at the Shape of a Sampling Distribution 178Case 1: The distribution of X is normal 178Case 2: The distribution of X is not normal—enter the Central Limit Theorem 178Finding Probabilities for the Sample Mean 181The Sampling Distribution of the Sample Proportion 183Finding Probabilities for the Sample Proportion 185Part 4: Guesstimating And Hypothesizing With Confidence 187Chapter 12: Leaving Room for a Margin of Error 189Seeing the Importance of That Plus or Minus 190Finding the Margin of Error: A General Formula 191Measuring sample variability 191Calculating margin of error for a sample proportion 193Reporting results 194Calculating margin of error for a sample mean 195Being confident you’re right 197Determining the Impact of Sample Size 197Sample size and margin of error 198Bigger isn’t always (that much) better! 198Keeping margin of error in perspective 199Chapter 13: Confidence Intervals: Making Your Best Guesstimate 201Not All Estimates Are Created Equal 202Linking a Statistic to a Parameter 203Getting with the Jargon 203Interpreting Results with Confidence 204Zooming In on Width 205Choosing a Confidence Level 206Factoring In the Sample Size 208Counting On Population Variability 209Calculating a Confidence Interval for a Population Mean 210Case 1: Population standard deviation is known 210Case 2: Population standard deviation is unknown and/or n is small 212Figuring Out What Sample Size You Need 213Determining the Confidence Interval for One Population Proportion 214Creating a Confidence Interval for the Difference of Two Means 216Case 1: Population standard deviations are known 216Case 2: Population standard deviations are unknown and/or sample sizes are small 218Estimating the Difference of Two Proportions 219Spotting Misleading Confidence Intervals 221Chapter 14: Claims, Tests, and Conclusions 223Setting Up the Hypotheses 224Defining the null 224What’s the alternative? 225Gathering Good Evidence (Data) 226Compiling the Evidence: The Test Statistic 226Gathering sample statistics 227Measuring variability using standard errors 227Understanding standard scores 228Calculating and interpreting the test statistic 228Weighing the Evidence and Making Decisions: p-Values 229Connecting test statistics and p-values 229Defining a p-value 230Calculating a p-value 230Making Conclusions 231Setting boundaries for rejecting Ho 232Testing varicose veins 233Assessing the Chance of a Wrong Decision 233Making a false alarm: Type-1 errors 234Missing out on a detection: Type-2 errors 234Chapter 15: Commonly Used Hypothesis Tests:Formulas and Examples 237Testing One Population Mean 238Handling Small Samples and Unknown Standard Deviations: The t-Test 240Putting the t-test to work 241Relating t to Z 241Handling negative t-values 242Examining the not-equal-to alternative 242Testing One Population Proportion 243Comparing Two (Independent) Population Averages 245Testing for an Average Difference (The Paired t-Test) 247Comparing Two Population Proportions 251Part 5: Statistical Studies And The Hunt For A Meaningful Relationship 255Chapter 16: Polls, Polls, and More Polls 257Recognizing the Impact of Polls 258Getting to the source 258Surveying what’s hot 260Impacting lives 260Behind the Scenes: The Ins and Outs of Surveys 262Planning and designing a survey 263Selecting the sample 266Carrying out a survey 268Interpreting results and finding problems 271Chapter 17: Experiments: Medical Breakthroughs or Misleading Results? 275Boiling Down the Basics of Studies 276Looking at the lingo of studies 276Observing observational studies 277Examining experiments 278Designing a Good Experiment 278Designing the experiment to make comparisons 279Selecting the sample size 281Choosing the subjects 283Making random assignments 283Controlling for confounding variables 284Respecting ethical issues 286Collecting good data 287Analyzing the data properly 289Making appropriate conclusions 290Making Informed Decisions 292Chapter 18: Looking for Links: Correlation and Regression 293Picturing a Relationship with a Scatterplot 294Making a scatterplot 295Interpreting a scatterplot 296Quantifying Linear Relationships Using the Correlation 297Calculating the correlation 297Interpreting the correlation 298Examining properties of the correlation 300Working with Linear Regression 301Figuring out which variable is X and which is Y 301Checking the conditions 302Calculating the regression line 302Interpreting the regression line 304Putting it all together with an example: The regression line for the crickets 306Making Proper Predictions 306Explaining the Relationship: Correlation versus Cause and Effect 308Chapter 19: Two-Way Tables and Independence 311Organizing a Two-Way Table 312Setting up the cells 313Figuring the totals 314Interpreting Two-Way Tables 315Singling out variables with marginal ­distributions 315Examining all groups — a joint distribution 317Comparing groups with conditional distributions 321Checking Independence and Describing Dependence 324Checking for independence 324Describing a dependent relationship 327Cautiously Interpreting Results 329Checking for legitimate cause and effect 329Projecting from sample to population 330Making prudent predictions 331Resisting the urge to jump to conclusions 332Part 6: The Part Of Tens 333Chapter 20: Ten Tips for the Statistically Savvy Sleuth 335Pinpoint Misleading Graphs 335Pie charts 336Bar graphs 336Time charts 337Histograms 339Uncover Biased Data 339Search for a Margin of Error 340Identify Non-Random Samples 341Sniff Out Missing Sample Sizes 342Detect Misinterpreted Correlations 343Reveal Confounding Variables 344Inspect the Numbers 344Report Selective Reporting 345Expose the Anecdote 346Chapter 21: Ten Surefire Exam Score Boosters 349Know What You Don’t Know, and then Do Something about It 350Avoid “Yeah-Yeah” Traps 351Yeah-yeah trap #1 352Yeah-yeah trap #2 352Make Friends with Formulas 354Make an “If-Then-How” Chart 355Figure Out What the Question Is Asking 357Label What You’re Given 358Draw a Picture 360Make the Connection and Solve the Problem 361Do the Math — Twice 362Analyze Your Answers 363Appendix: Tables For Reference 365Index 375